# Symmetric matrix is not symmetric

**URL:** <https://discourse.julialang.org/t/symmetric-matrix-is-not-symmetric/55479>\
**Category:** General Usage\
**Tags:** question, linearalgebra, distances\
**Created:** [February 17, 2021, 5:44pm UTC](https://discourse.julialang.org/t/symmetric-matrix-is-not-symmetric/55479 "2021-02-17T17:44:24Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![kevbonham](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kevbonham/32/216165_2.png) [@kevbonham](https://discourse.julialang.org/u/kevbonham)\
**Post date:** [February 17, 2021, 5:44pm UTC](https://discourse.julialang.org/t/symmetric-matrix-is-not-symmetric/55479/1 "2021-02-17T17:44:24Z")

</div>

I’m trying to do a hierarchical clustering of a matrix, and I’m running into a weird problem. Using `Distances.jl`, I’m doing `dm = pairwise(Jaccard(), my_matrix)`, and then `hclust(dm)` from `Clustering.jl`. But I’m getting

```julia
julia> rowclust = hclust(rowdm)
ERROR: ArgumentError: Distance matrix should be symmetric.

```

When I use `issymetric` from `LinearAlgebra`, sure enough

```julia
julia> issymmetric(rowdm)
false

```

But I’m pretty sure `pairwise` from Distances should always return a symmetric matrix when the distance function is metric (which Jaccard is), and when I looked for which element is mismatched

```julia
julia> for i in 1:size(rowdm, 1), j in 1:size(rowdm, 2)
           j<i && continue
           if rowdm[i,j] !== rowdm[j, i]
               @info "mismatch!" i, j, rowdm[i,j], rowdm[j,i]
           end
       end

julia>

```

They all seem to be correct. Am I misunderstanding what a symmetric matrix is? And how this function of Distances.jl works? For what it’s worth, I’m trying to cluster along both columns and rows of my matrix, and the former works as expected. I also haven’t been able to come up with a MWE that throws the same error.

EDIT: `Euclidean()` distance for the rows seems to work 🤔

---

<div class="post-metadata">

**Author:** ![dilumaluthge](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dilumaluthge/32/29283_2.png) [@dilumaluthge](https://discourse.julialang.org/u/dilumaluthge)\
**Post date:** [February 17, 2021, 6:13pm UTC](https://discourse.julialang.org/t/symmetric-matrix-is-not-symmetric/55479/2 "2021-02-17T18:13:29Z")

</div>

What’s the type of `rowdm`?

Also, what do you get if you do `rowdm - transpose(rowdm)` and `rowdm - adjoint(rowdm)`?

---

<div class="post-metadata">

**Author:** ![kevbonham](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kevbonham/32/216165_2.png) [@kevbonham](https://discourse.julialang.org/u/kevbonham)\
**Post date:** [February 17, 2021, 6:26pm UTC](https://discourse.julialang.org/t/symmetric-matrix-is-not-symmetric/55479/3 "2021-02-17T18:26:08Z")

</div>

```julia
julia> eltype(rowdm)
Float64

julia> typeof(rowdm)
Matrix{Float64} (alias for Array{Float64, 2})

julia> rowdm - adjoint(rowdm)
1092×1092 Matrix{Float64}:
#...

julia> all(==(0), rowdm - adjoint(rowdm))
false

julia> rowdm - adjoint(rowdm)
1092×1092 Matrix{Float64}:
 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 … 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

julia> rowdm[findall(!=(0), rowdm - adjoint(rowdm))]
3540-element Vector{Float64}:
 NaN
 NaN
 NaN
 NaN
 NaN
 NaN
#...

```

Looks like a bunch of NaNs 🤯

```julia
julia> count(isnan, rowdm)
3540

```

Didn’t know that was possible with Jaccard… Oh well, replacing those fixes things, thanks!